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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 138, Pages 82–98 (Mi into216)

On general production of entropy in open Markov quantum systems

A. S. Trushechkinabc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b National Engineering Physics Institute "MEPhI", Moscow
c National University of Science and Technology «MISIS»

Abstract: We discuss production of entropy per unit time for a quantum system governed by the Lindblad equation. The difficulty is as follows: in order to determine the total production of entropy, one must know the entropy flow from the system into the environment. This requires additional information on the environment and on its interaction with the system. The Lindblad equation for the reduced density matrix of the system does not contain such information. Therefore, the following question arises: What minimum additional information about the environment must be added to the Lindblad equation in order to find the flow of entropy into the environment and the total production of entropy? To answer this question, we use the concept of a complementary quantum channel known from the the quantum information theory. We also prove a theorem on the nonnegativity of production of entropy, and, under certain assumptions, the adiabatic and nonadiabatic contribution to it.

Keywords: open quantum systems, Lindblad equation, production of entropy, second law of thermodynamics.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÌÊ-2815.2017.1 This work was supported by the Grant of the President of the Russian Federation (project MK-2815.2017.1).

Full text: PDF file (273 kB)

English version:
Journal of Mathematical Sciences, 2019, 241:2, 191–209

Bibliographic databases:

UDC: 517.958:530.145, 536.73, 536.75
MSC: 81S22, 82C10

Citation: A. S. Trushechkin, “On general production of entropy in open Markov quantum systems”, Quantum computing, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 82–98; Journal of Mathematical Sciences, 241:2 (2019), 191–209

Citation in format AMSBIB
\Bibitem{Tru17} \by A.~S.~Trushechkin \paper On general production of entropy in open Markov quantum systems \inbook Quantum computing \serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. \yr 2017 \vol 138 \pages 82--98 \publ VINITI \publaddr Moscow \mathnet{http://mi.mathnet.ru/into216} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3801253} \zmath{https://zbmath.org/?q=an:1426.81045} \transl \jour Journal of Mathematical Sciences \yr 2019 \vol 241 \issue 2 \pages 191--209 \crossref{https://doi.org/10.1007/s10958-019-04417-4} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. E. Teretenkov, “Quadratic Fermionic Dynamics with Dissipation”, Math. Notes, 102:6 (2017), 846–854
2. A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271
3. A. E. Teretenkov, “Dynamics of Moments for Quadratic GKSL Generators”, Math. Notes, 106:1 (2019), 151–155
4. A. S. Trushechkin, “Dynamics of Reservoir Observables within the Zwanzig Projection Operator Method in the Theory of Open Quantum Systems”, Proc. Steklov Inst. Math., 306 (2019), 257–270
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